IACM Colloquium
Speaker:
Prof. Vassilios Kalpakides
Title:
A convolutional Hamilton Principle for Discrete and Continuous Systems
Abstract:
The standard Hamilton principle presents some deficiencies concerning the mathematical description of dynamical problems. The first one is related with the lack of compatibility between the necessary for the Hamilton principle temporal conditions and the initial conditions of the corresponding initial value problem. The second deficiency concerns the well—known and widely—discussed subject of dissipative systems, where the differential equation of a non—conservative problem can’t be extracted from the standard Hamilton principle. Very often, ad hoc variational tricks are used to overcome this deficiency so as the right differential equation to be achieved.
A novel approach will be presented to overcome the above—mentioned deficiencies. It is based on the use of the convolution instead of the
L^2 inner product as well as on the introduction of fractional derivatives in the action functional. Finally, it comes out a variational principle of Hamilton type which fully reproduces the corresponding initial value problem (or the initial-boundary value problem in the case of an infinite dimensional system). In this perspective, such a variational principle paves the way for a finite element method for initial value problems.
Short Bio:
Vassilios Kalpakides is a professor in the School of Applied Mathematics and Physical Sciences at the National Technical University of Athens. He graduated from the Mathematical Department of the University of Ioannina where he has got the PhD degree as well. He has worked for a long period as a faculty member at the departments of Mathematics and Materials Science and Engineering at the University of Ioannina as well as a visiting professor for short periods in Technical University of Vienna, Pierre et Marie Curie—Paris 6 and Istanbul Technical University. His research interests are focus mainly on theoretical aspects of continuum mechanics.
Time & Date:
15:00, Thursday 16th of June 2022
Zoom Info:
https://us06web.zoom.us/j/7761040361?pwd=dEs4TFZxck01Vk5PQWR1TUxKdndwUT09
Meeting ID: 776 104 0361
Passcode: 787479
Host:
Dimitrios Sfyris